The present invention relates to a Jacobian group element adder, and more particularly technology for discrete logarithmic cryptography employing a Jacobian group of an algebraic curve (hereinafter, referred to as algebraic curve cryptography) that is a kind of the discrete logarithmic cryptography, which is cryptography technology as information security technology.
It is an elliptic curve cryptography that has come in practice most exceedingly among the algebraic curve cryptography. However, an elliptic curve for use in the elliptic curve cryptography is a very special one as compared with a general algebraic curve. There is the apprehension that an aggressive method of exploiting its specialty would be discovered in the near future. For this, so as to secure safety more reliably, a general algebraic curve of which specialty is lower is desirably employed. Cab curve cryptography is known as an algebraic curve cryptography capable of employing a more general algebraic curve as mentioned above.
The Cab curve cryptography, however, is less employed in the industrial field as compared with the elliptic curve cryptography. Its main reason is that the conventional additive algorithm in the Jacobian group of the conventional Cab curve is tens of times slower than additive algorithm in the Jacobian group of the elliptic curve, and as a result, process efficiency of encryption/decryption in the Cab curve cryptography is remarkably inferior as compared with the elliptic curve cryptography, which was shown in “Jacobian Group Additive algorithm of Cab Curve and its Application to Discrete Logarithmic Cryptography” by Seigo Arita, Japanese-version collection of The Institute of Electronics, Information and Communication Engineers, Vol. J82-A, No.8, pp.1291–1299, 1999.
Also, another additive algorithm in the Jacobian group of the Cab curve was proposed in “A Fast Jacobian Group Arithmetic Scheme for Algebraic Curve Cryptography” by Ryuichi Harasawa, and Joe Suzuki, Vol. E84-A No.1, pp.130–139, 2001 as well; however, even though an asymptotic calculation quantity of algorithm was given, no execution speed data in a packaging experiment was shown, and, also, no report on the packaging experiment by a third party was provided, and the extent to which the execution speed can practically be achieved is uncertain.
As seen from the foregoing, non-efficiency of the additive algorithm in the Jacobian group of the Cab curve prevents the cryptography of the above curve from coming in practice, which gives rise to the necessity of executing addition in the Jacobian group of the Cab curve at a high speed.